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Theorem vtocle 3431
Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 9-Sep-1993.)
Hypotheses
Ref Expression
vtocle.1 𝐴 ∈ V
vtocle.2 (𝑥 = 𝐴𝜑)
Assertion
Ref Expression
vtocle 𝜑
Distinct variable groups:   𝑥,𝐴   𝜑,𝑥

Proof of Theorem vtocle
StepHypRef Expression
1 vtocle.1 . 2 𝐴 ∈ V
2 vtocle.2 . . 3 (𝑥 = 𝐴𝜑)
32vtocleg 3428 . 2 (𝐴 ∈ V → 𝜑)
41, 3ax-mp 5 1 𝜑
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1630  wcel 2144  Vcvv 3349
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-12 2202  ax-ext 2750
This theorem depends on definitions:  df-bi 197  df-an 383  df-tru 1633  df-ex 1852  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-v 3351
This theorem is referenced by:  zfrepclf  4908  tz6.12i  6355  eloprabga  6893  cfflb  9282  axcc3  9461  nn0ind-raph  11678  finxpreclem6  33563
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